Question

in a parallelogram WXYZ, <W=70°,find the measure of each of the angles <X, <Y,and <Z.

Answer 1

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Answer 2

Concept:

A parallelogram is a quadrilateral with parallel and equal sides on both pairs of opposite sides.

Given:

In parallelogram WXYZ, ∠W=70°.

Find:

The measures of each of the angles ∠X, ∠Y, and ∠Z.

Solution:

In parallelogram WXYZ, ∠Y = ∠W

(∵ Opposite angles of parallelogram are equal.)

∴ ∠Y = 70°.

∠W + ∠Z = 180°

(∵ Consecutive angles are supplementary.)

∠Z + 70° = 180°

∠Z = 110°

∠X = ∠Z

(∵ Opposite angles are equal.)

∠X = 110°

Hence all the angles of the parallelogram WXYZ are

∠W = 70°

∠X = 110°

∠Y = 70°

∠Z = 110°